Multi-branch entrainment and multi-peaked order-functions in a phase model of limit-cycle oscillators with uniform all-to-all coupling

A peculiar type of mutual entrainment is found numerically in a phase model of a large population of limit-cycle oscillators with uniform all-to-all coupling strongly modulated by higher harmonics, in which more than one branch of mutually phase-locked oscillators exists, accompanied by a multi-peaked order function. For system size N, at least eN different entrained states are likely to coexist with almost identical order functions. Also discussed is how to extend the order-function theory for dealing with such a phenomenon.